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Answer :
To find the approximate length of the arc intersected by a central angle in a circle, we can use the formula for the arc length:
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \theta \)[/tex] is the central angle in radians.
Let's go through the steps to find the arc length:
1. Identify the given values:
- The radius [tex]\( r \)[/tex] of the circle is 10 inches.
- The central angle [tex]\( \theta \)[/tex] is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the arc length formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate the product:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3}
\][/tex]
4. Convert the arc length into a numeric approximation:
- Using the approximation [tex]\(\pi \approx 3.14159\)[/tex], multiply:
[tex]\[
\text{Arc Length} \approx \frac{20 \times 3.14159}{3}
\][/tex]
- Calculate the result:
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
Therefore, the approximate length of the arc is 20.94 inches. This corresponds to the choice 20.94 inches from the given options.
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \theta \)[/tex] is the central angle in radians.
Let's go through the steps to find the arc length:
1. Identify the given values:
- The radius [tex]\( r \)[/tex] of the circle is 10 inches.
- The central angle [tex]\( \theta \)[/tex] is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the arc length formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate the product:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3}
\][/tex]
4. Convert the arc length into a numeric approximation:
- Using the approximation [tex]\(\pi \approx 3.14159\)[/tex], multiply:
[tex]\[
\text{Arc Length} \approx \frac{20 \times 3.14159}{3}
\][/tex]
- Calculate the result:
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
Therefore, the approximate length of the arc is 20.94 inches. This corresponds to the choice 20.94 inches from the given options.
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Rewritten by : Jeany
